This is the only way I was able to control (turn on/off) my green laser module with my Arduino board. I made the same mistake other people have made connecting the laser module directly to the board, which, for some reason does not work.

Off the top of my head I don't know the pinout for the TIP120 but assuming you have the transistor in correctly you should have a resistor from the Arduino to the base (no resistor is shown). Collector to the laser and emitter to GND.

Also, how much current does the laser draw? Maybe the Arduino regulator is objecting.______Rob

There is a ambiguity, on picture they install IRF510 or IRF520 MOSFET,as you can see marking "FET" on the body of the transistor.And FET doesn't require resistor, as no DC current.It bad practice, IMHO resistor has to be any way, to limitcharging gate-source capacitor current. On low frequencies arduino will survive such mistreatment at least.

But in description to the picture:"Connect the base to an output pin of the microcontroller, and the emitter to ground like so: "

That is WRONG.,If transistor is MOSFET, description must be:"Connect the GATE to an output pin of the microcontroller, and the SOURCE to ground like so: "